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INTRODUCTION 1
1
Introduction
M. Suzanne Donovan and John D. Bransford
More than any other species, people are designed to be flexible learners
and, from infancy, are active agents in acquiring knowledge and skills. People
can invent, record, accumulate, and pass on organized bodies of knowledge
that help them understand, shape, exploit, and ornament their environment.
Much that each human being knows about the world is acquired informally,
but mastery of the accumulated knowledge of generations requires inten-
tional learning, often accomplished in a formal educational setting.
Decades of work in the cognitive and developmental sciences has pro-
vided the foundation for an emerging science of learning. This foundation
offers conceptions of learning processes and the development of competent
performance that can help teachers support their students in the acquisition
of knowledge that is the province of formal education. The research litera-
ture was synthesized in the National Research Council report How People
Learn: Brain, Mind, Experience, and School.1 In this volume, we focus on
three fundamental and well-established principles of learning that are high-
lighted in How People Learn and are particularly important for teachers to
understand and be able to incorporate in their teaching:
1. Students come to the classroom with preconceptions about how the
world works. If their initial understanding is not engaged, they may fail to
grasp the new concepts and information, or they may learn them for pur-
poses of a test but revert to their preconceptions outside the classroom.
2. To develop competence in an area of inquiry, students must (a) have
a deep foundation of factual knowledge, (b) understand facts and ideas in
the context of a conceptual framework, and (c) organize knowledge in ways
that facilitate retrieval and application.

4 HOW STUDENTS LEARN
Principle #1: Engaging Prior Understandings
What Lionni's story captures so effectively is a fundamental insight about
learning: new understandings are constructed on a foundation of existing
understandings and experiences. With research techniques that permit the
study of learning in infancy and tools that allow for observation of activity in
the brain, we understand as never before how actively humans engage in
learning from the earliest days of life (see Box 1-1). The understandings
children carry with them into the classroom, even before the start of formal
schooling, will shape significantly how they make sense of what they are
BOX 1-1 The Development of Physical Concepts in Infancy
Research studies have demonstrated that infants as young as 3 to 4 months of
age develop understandings and expectations about the physical world. For ex-
ample, they understand that objects need support to prevent them from falling to
the ground, that stationary objects may be displaced when they come into contact
with moving objects, and that objects at rest must be propelled into motion.3
In research by Needham and Baillargeon,4infants were shown a table on which
a box rested. A gloved hand reached out from a window beside the table and
placed another box in one of two locations: on top of the first box (the possible
event), and beyond the box--creating the impression that the box was suspended
in midair. In this and similar studies, infants look reliably longer at the impossible
events, suggesting an awareness and a set of expectations regarding what is and
is not physically possible.
SOURCE: Needham and Baillargeon (1993). Reprinted with permission from
Elsevier.

INTRODUCTION 5
BOX 1-2 Misconceptions About Momentum
Andrea DiSessa5 conducted a study in which he compared the performance of
college physics students at a top technological university with that of elementary
schoolchildren on a task involving momentum. He instructed both sets of students
to play a computerized game that required them to direct a simulated object (a
dynaturtle) so that it would hit a target, and to do so with minimum speed at im-
pact. Participants were introduced to the game and given a hands-on trial that al-
lowed them to apply a few taps with a wooden mallet to a ball on a table before
they began.
DiSessa found that both groups of students failed miserably at the task. De-
spite their training, college physics majors--just like the elementary school chil-
dren--applied the force when the object was just below the target, failing to take
momentum into account. Further investigation with one college student revealed
that she knew the relevant physical properties and formulas and would have per-
formed well on a written exam. Yet in the context of the game, she fell back on her
untrained conceptions of how the physical world works.
taught. Just as the fish constructed an image of a human as a modified fish,
children use what they know to shape their new understandings.
While prior learning is a powerful support for further learning, it can
also lead to the development of conceptions that can act as barriers to learn-
ing. For example, when told that the earth is round, children may look to
reconcile this information with their experience with balls. It seems obvious
that one would fall off a round object. Researchers have found that some
children solve the paradox by envisioning the earth as a pancake, a "round"
shape with a surface on which people could walk without falling off.6
How People Learn summarizes a number of studies demonstrating the
active, preconception-driven learning that is evident in humans from infancy
through adulthood.7 Preconceptions developed from everyday experiences
are often difficult for teachers to change because they generally work well
enough in day-to-day contexts. But they can impose serious constraints on
understanding formal disciplines. College physics students who do well on
classroom exams on the laws of motion, for example, often revert to their
untrained, erroneous models outside the classroom. When they are con-
fronted with tasks that require putting their knowledge to use, they fail to
take momentum into account, just as do elementary students who have had
no physics training (see Box 1-2). If students' preconceptions are not ad-
dressed directly, they often memorize content (e.g., formulas in physics), yet
still use their experience-based preconceptions to act in the world.

6 HOW STUDENTS LEARN
Principle #2: The Essential Role of Factual Knowledge
and Conceptual Frameworks in Understanding
The Fish Is Fish story also draws attention to the kinds of knowledge,
factual and conceptual, needed to support learning with understanding. The
frog in the story provides information to the fish about humans, birds, and
cows that is accurate and relevant, yet clearly insufficient. Feathers, legs,
udders, and sport coats are surface features that distinguish each species.
But if the fish (endowed now with human thinking capacity) is to under-
stand how the land species are different from fish and different from each
other, these surface features will not be of much help. Some additional,
critical concepts are needed--for example, the concept of adaptation. Spe-
cies that move through the medium of air rather than water have a different
mobility challenge. And species that are warm-blooded, unlike those that
are cold-blooded, must maintain their body temperature. It will take more
explaining of course, but if the fish is to see a bird as something other than
a fish with feathers and wings and a human as something other than an
upright fish with clothing, then feathers and clothing must be seen as adap-
tations that help solve the problem of maintaining body temperature, and
upright posture and wings must be seen as different solutions to the prob-
lem of mobility outside water.
Conceptual information such as a theory of adaptation represents a kind
of knowledge that is unlikely to be induced from everyday experiences. It
typically takes generations of inquiry to develop this sort of knowledge, and
people usually need some help (e.g., interactions with "knowledgeable oth-
ers") to grasp such organizing concepts.8
Lionni's fish, not understanding the described features of the land ani-
mals as adaptations to a terrestrial environment, leaps from the water to
experience life on land for himself. Since he can neither breathe nor maneu-
ver on land, the fish must be saved by the amphibious frog. The point is well
illustrated: learning with understanding affects our ability to apply what is
learned (see Box 1-3).
This concept of learning with understanding has two parts: (1) factual
knowledge (e.g., about characteristics of different species) must be placed
in a conceptual framework (about adaptation) to be well understood; and
(2) concepts are given meaning by multiple representations that are rich in
factual detail. Competent performance is built on neither factual nor concep-
tual understanding alone; the concepts take on meaning in the knowledge-
rich contexts in which they are applied. In the context of Lionni's story, the
general concept of adaptation can be clarified when placed in the context of
the specific features of humans, cows, and birds that make the abstract
concept of adaptation meaningful.

INTRODUCTION 7
BOX 1-3 Learning with Understanding Supports Knowledge
Use in New Situations
In one of the most famous early studies comparing the effects of "learning a proce-
dure" with "learning with understanding," two groups of children practiced throw-
ing darts at a target underwater.9 One group received an explanation of refraction of
light, which causes the apparent location of the target to be deceptive. The other
group only practiced dart throwing, without the explanation. Both groups did equally
well on the practice task, which involved a target 12 inches under water. But the
group that had been instructed about the abstract principle did much better when
they had to transfer to a situation in which the target was under only 4 inches of
water. Because they understood what they were doing, the group that had received
instruction about the refraction of light could adjust their behavior to the new task.
This essential link between the factual knowledge base and a concep-
tual framework can help illuminate a persistent debate in education: whether
we need to emphasize "big ideas" more and facts less, or are producing
graduates with a factual knowledge base that is unacceptably thin. While
these concerns appear to be at odds, knowledge of facts and knowledge of
important organizing ideas are mutually supportive. Studies of experts and
novices--in chess, engineering, and many other domains--demonstrate that
experts know considerably more relevant detail than novices in tasks within
their domain and have better memory for these details (see Box 1-4). But the
reason they remember more is that what novices see as separate pieces of
information, experts see as organized sets of ideas.
Engineering experts, for example, can look briefly at a complex mass of
circuitry and recognize it as an amplifier, and so can reproduce many of its
circuits from memory using that one idea. Novices see each circuit sepa-
rately, and thus remember far fewer in total. Important concepts, such as
that of an amplifier, structure both what experts notice and what they are
able to store in memory. Using concepts to organize information stored in
memory allows for much more effective retrieval and application. Thus, the
issue is not whether to emphasize facts or "big ideas" (conceptual knowl-
edge); both are needed. Memory of factual knowledge is enhanced by con-
ceptual knowledge, and conceptual knowledge is clarified as it is used to
help organize constellations of important details. Teaching for understand-
ing, then, requires that the core concepts such as adaptation that organize
the knowledge of experts also organize instruction. This does not mean that
that factual knowledge now typically taught, such as the characteristics of
fish, birds, and mammals, must be replaced. Rather, that factual information
is given new meaning and a new organization in memory because those
features are seen as adaptive characteristics.

8 HOW STUDENTS LEARN
BOX 1-4Experts Remember Considerably More Relevant Detail Than
Novices in Tasks Within Their Domain

INTRODUCTION 9
In one study, a chess master, a Class A player (good but not a master),
and a novice were given 5 seconds to view a chess board position from
the middle of a chess game (see below).
After 5 seconds the board was covered, and each participant at-
tempted to reconstruct the board position on another board. This proce-
dure was repeated for multiple trials until everyone received a perfect
score. On the first trial, the master player correctly placed many more
pieces than the Class A player, who in turn placed more than the novice:
16, 8, and 4, respectively. (See data graphed below.)
However, these results occurred only when the chess pieces were
arranged in configurations that conformed to meaningful games of chess.
When chess pieces were randomized and presented for 5 seconds, the
recall of the chess master and Class A player was the same as that of the
novice--they all placed 2 to 3 positions correctly. The apparent difference
in memory capacity is due to a difference in pattern recognition. What the
expert can remember as a single meaningful pattern, novices must re-
member as separate, unrelated items.
25
20
recalled
15 Master
Class A player
10
Beginner
correctly
5
0
Pieces
1 2 3 4 5 6 7
Trial
SOURCE: Chase and Simon (1973). Reprinted with permission from Elsevier.

10 HOW STUDENTS LEARN
Principle #3: The Importance of Self-Monitoring
Hero though he is for saving the fish's life, the frog in Lionni's story gets
poor marks as a teacher. But the burden of learning does not fall on the
teacher alone. Even the best instructional efforts can be successful only if the
student can make use of the opportunity to learn. Helping students become
effective learners is at the heart of the third key principle: a "metacognitive"
or self-monitoring approach can help students develop the ability to take
control of their own learning, consciously define learning goals, and moni-
tor their progress in achieving them. Some teachers introduce the idea of
metacognition to their students by saying, "You are the owners and opera-
tors of your own brain, but it came without an instruction book. We need to
learn how we learn."
"Meta" is a prefix that can mean after, along with, or beyond. In the
psychological literature, "metacognition" is used to refer to people's knowl-
edge about themselves as information processors. This includes knowledge
about what we need to do in order to learn and remember information (e.g.,
most adults know that they need to rehearse an unfamiliar phone number to
keep it active in short-term memory while they walk across the room to dial
the phone). And it includes the ability to monitor our current understanding
to make sure we understand (see Box 1-5). Other examples include moni-
toring the degree to which we have been helpful to a group working on a
project.10
BOX 1-5 Metacognitive Monitoring: An Example
Read the following passage from a literary critic, and pay attention to the strategies you
use to comprehend:
If a serious literary critic were to write a favorable, full-length review of How Could I Tell
Mother She Frightened My Boyfriends Away, Grace Plumbuster's new story, his startled read-
ers would assume that he had gone mad, or that Grace Plumbuster was his editor's wife.
Most good readers have to back up several times in order to grasp the meaning of
this passage. In contrast, poor readers tend to simply read it all the way through without
pausing and asking if the passage makes sense. Needless to say, when asked to para-
phrase the passage they fall short.
SOURCE: Whimbey and Whimbey (1975, p. 42).

INTRODUCTION 11
In Lionni's story, the fish accepted the information about life on land
rather passively. Had he been monitoring his understanding and actively
comparing it with what he already knew, he might have noted that putting
on a hat and jacket would be rather uncomfortable for a fish and would slow
his swimming in the worst way. Had he been more engaged in figuring out
what the frog meant, he might have asked why humans would make them-
selves uncomfortable and compromise their mobility. A good answer to his
questions might have set the stage for learning about differences between
humans and fish, and ultimately about the notion of adaptation. The con-
cept of metacognition includes an awareness of the need to ask how new
knowledge relates to or challenges what one already knows--questions that
stimulate additional inquiry that helps guide further learning.11
The early work on metacognition was conducted with young children
in laboratory contexts.12 In studies of "metamemory," for example, young
children might be shown a series of pictures (e.g., drum, tree, cup) and
asked to remember them after 15 seconds of delay (with the pictures no
longer visible). Adults who receive this task spontaneously rehearse during
the 15-second interval. Many of the children did not. When they were ex-
plicitly told to rehearse, they would do so, and their memory was very good.
But when the children took part in subsequent trials and were not reminded
to rehearse, many failed to rehearse even though they were highly moti-
vated to perform well in the memory test. These findings suggest that the
children had not made the "metamemory" connection between their re-
hearsal strategies and their short-term memory abilities.13
Over time, research on metacognition (of which metamemory is consid-
ered a subset) moved from laboratory settings to the classroom. One of the
most striking applications of a metacognitive approach to instruction was
pioneered by Palincsar and Brown in the context of "reciprocal teaching."14
Middle school students worked in groups (guided by a teacher) to help one
another learn to read with understanding. A key to achieving this goal in-
volves the ability to monitor one's ongoing comprehension and to initiate
strategies such as rereading or asking questions when one's comprehension
falters. (Box 1-5 illustrates this point.) When implemented appropriately,
reciprocal teaching has been shown to have strong effects on improving
students' abilities to read with understanding in order to learn.
Appropriate kinds of self-monitoring and reflection have been demon-
strated to support learning with understanding in a variety of areas. In one
study,15 for example, students who were directed to engage in self-explana-
tion as they solved mathematics problems developed deeper conceptual
understanding than did students who solved those same problems but did
not engage in self-explanation. This was true even though the common time
limitation on both groups meant that the self-explaining students solved
fewer problems in total.

12 HOW STUDENTS LEARN
Helping students become more metacognitive about their own thinking
and learning is closely tied to teaching practices that emphasize self-assess-
ment. The early work of Thorndike16 demonstrated that feedback is impor-
tant for learning. However, there is a difference between responding to
feedback that someone else provides and actively seeking feedback in order
to assess one's current levels of thinking and understanding. Providing sup-
port for self-assessment is an important component of effective teaching.
This can include giving students opportunities to test their ideas by building
things and seeing whether they work, performing experiments that seek to
falsify hypotheses, and so forth. Support for self-assessment is also provided
by opportunities for discussion where teachers and students can express
different views and explore which ones appear to make the most sense.
Such questioning models the kind of dialogue that effective learners inter-
nalize. Helping students explicitly understand that a major purpose of these
activities is to support metacognitive learning is an important component of
successful teaching strategies.17
Supporting students to become aware of and engaged in their own
learning will serve them well in all learning endeavors. To be optimally
effective, however, some metacognitive strategies need to be taught in the
context of individual subject areas. For example, guiding one's learning in a
particular subject area requires awareness of the disciplinary standards for
knowing. To illustrate, asking the question "What is the evidence for this
claim?" is relevant whether one is studying history, science, or mathematics.
However, what counts as evidence often differs. In mathematics, for ex-
ample, formal proof is very important. In science, formal proofs are used
when possible, but empirical observations and experimental data also play a
major role. In history, multiple sources of evidence are sought and attention
to the perspective from which an author writes and to the purpose of the
writing is particularly important. Overall, knowledge of the discipline one is
studying affects people's abilities to monitor their own understanding and
evaluate others' claims effectively.
LEARNING ENVIRONMENTS AND THE DESIGN
OF INSTRUCTION
The key principles of learning discussed above can be organized into a
framework for thinking about teaching, learning, and the design of class-
room and school environments. In How People Learn, four design character-
istics are described that can be used as lenses to evaluate the effectiveness of
teaching and learning environments. These lenses are not themselves re-
search findings; rather, they are implications drawn from the research base:

INTRODUCTION 13
Community
Learner Knowledge
centered centered
Assessment
centered
FIGURE 1-1 Perspectives on learning environments.
· The learner-centered lens encourages attention to preconceptions,
and begins instruction with what students think and know.
· The knowledge-centered lens focuses on what is to be taught, why it
is taught, and what mastery looks like.
· The assessment-centered lens emphasizes the need to provide fre-
quent opportunities to make students' thinking and learning visible as a
guide for both the teacher and the student in learning and instruction.
· The community-centered lens encourages a culture of questioning,
respect, and risk taking.
These aspects of the classroom environment are illustrated in Figure 1-1
and are discussed below.

14 HOW STUDENTS LEARN
Learner-Centered Classroom Environments
Instruction must begin with close attention to students' ideas, knowl-
edge, skills, and attitudes, which provide the foundation on which new
learning builds. Sometimes, as in the case of Lionni's fish, learners' existing
ideas lead to misconceptions. More important, however, those existing con-
ceptions can also provide a path to new understandings. Lionni's fish mis-
takenly projects the model of a fish onto humans, birds, and cows. But the
fish does know a lot about being a fish, and that experience can provide a
starting point for understanding adaptation. How do the scales and fins of a
fish help it survive? How would clothing and feathers affect a fish? The fish's
existing knowledge and experience provide a route to understanding adap-
tation in other species. Similarly, the ideas and experiences of students pro-
vide a route to new understandings both about and beyond their experi-
ence.
Sometimes the experiences relevant to teaching would appear to be
similar for all students: the ways in which forces act on a falling ball or
feather, for example. But students in any classroom are likely to differ in
how much they have been encouraged to observe, think about, or talk
about a falling ball or feather. Differences may be larger still when the sub-
ject is a social rather than a natural phenomenon because the experiences
themselves, as well as norms regarding reflection, expression, and interac-
tion, differ for children from different families, communities, and cultures.
Finally, students' expectations regarding their own performances, including
what it means to be intelligent, can differ in ways that affect their persistence
in and engagement with learning.
Being learner-centered, then, involves paying attention to students' back-
grounds and cultural values, as well as to their abilities. To build effectively
on what learners bring to the classroom, teachers must pay close attention
to individual students' starting points and to their progress on learning
tasks. They must present students with "just-manageable difficulties"--chal-
lenging enough to maintain engagement and yet not so challenging as to
lead to discouragement. They must find the strengths that will help students
connect with the information being taught. Unless these connections are
made explicitly, they often remain inert and so do not support subsequent
learning.
Knowledge-Centered Classroom Environments
While the learner-centered aspects of the classroom environment focus
on the student as the starting point, the knowledge-centered aspects focus
on what is taught (subject matter), why it is taught (understanding), how
the knowledge should be organized to support the development of exper-

INTRODUCTION 15
tise (curriculum), and what competence or mastery looks like (learning
goals). Several important questions arise when one adopts the knowledge-
centered lens:
· What is it important for students to know and be able to do?
· What are the core concepts that organize our understanding of this
subject matter, and what concrete cases and detailed knowledge will allow
students to master those concepts effectively?
· How will we know when students achieve mastery?18 This question
overlaps the knowledge-centered and assessment-centered lenses.
An important point that emerges from the expert­novice literature is
the need to emphasize connected knowledge that is organized around the
foundational ideas of a discipline. Research on expertise shows that it is
the organization of knowledge that underlies experts' abilities to under-
stand and solve problems.19 Bruner, one of the founding fathers of the
new science of learning, has long argued the importance of this insight to
education:20
The curriculum of a subject should be determined by the most fundamental
understanding that can be achieved of the underlying principles that give
structure to a subject. Teaching specific topics or skills without making
clear their context in the broader fundamental structure of a field of knowl-
edge is uneconomical. . . . An understanding of fundamental principles and
ideas appears to be the main road to adequate transfer of training. To
understand something as a specific instance of a more general case--which
is what understanding a more fundamental structure means--is to have
learned not only a specific thing but also a model for understanding other
things like it that one may encounter.
Knowledge-centered and learner-centered environments intersect when
educators take seriously the idea that students must be supported to de-
velop expertise over time; it is not sufficient to simply provide them with
expert models and expect them to learn. For example, intentionally organiz-
ing subject matter to allow students to follow a path of "progressive differen-
tiation" (e.g., from qualitative understanding to more precise quantitative
understanding of a particular phenomenon) involves a simultaneous focus
on the structure of the knowledge to be mastered and the learning process
of students.21
In a comparative study of the teaching of mathematics in China and the
United States, Ma sought to understand why Chinese students outperform
students from the United States in elementary mathematics, even though
teachers in China often have less formal education. What she documents is

16 HOW STUDENTS LEARN
that Chinese teachers are far more likely to identify core mathematical con-
cepts (such as decomposing a number in subtraction with regrouping), to
plan instruction to support mastery of the skills and knowledge required for
conceptual understanding, and to use those concepts to develop clear con-
nections across topics (see Box 1-6).
If identifying a set of "enduring connected ideas" is critical to effective
educational design, it is a task not just for teachers, but also for the develop-
ers of curricula, text books, and other instructional materials; universities
and other teacher preparation institutions; and the public and private groups
involved in developing subject matter standards for students and their teach-
ers. There is some good work already in place, but much more needs to be
done. Indeed, an American Association for the Advancement of Science
review of middle school and high school science textbooks found that al-
though a great deal of detailed and sophisticated material was presented,
very little attention was given to the concepts that support an understanding
of the discipline.22
The three history chapters in this volume describe core ideas in teaching
about exploration and discovery that support conceptual understanding and
that connect that particular topic to the larger discipline: the concepts of
historical evidence and perspective in history. Because textbooks sometimes
focus primarily on facts and details and neglect organizing principles, creat-
ing a knowledge-centered classroom will often require that a teacher go
beyond the textbook to help students see a structure to the knowledge,
mainly by introducing them to essential concepts. These chapters provide
examples of how this might be done.
Assessment-Centered Classroom Environments
Formative assessments--ongoing assessments designed to make students'
thinking visible to both teachers and students--are essential. Assessments
are a central feature of both a learner-centered and a knowledge-centered
classroom. They permit the teacher to grasp students' preconceptions, which
is critical to working with and building on those notions. Once the knowl-
edge to be learned is well defined, assessment is required to monitor stu-
dent progress (in mastering concepts as well as factual information), to un-
derstand where students are in the developmental path from informal to
formal thinking, and to design instruction that is responsive to student progress.
An important feature of the assessment-centered classroom is assess-
ment that supports learning by providing students with opportunities to
revise and improve their thinking.23 Such assessments help students see
their own progress over time and point to problems that need to be ad-
dressed in instruction. They may be quite informal. A physics teacher, for
example, reports showing students who are about to study structure a video

INTRODUCTION 17
clip of a bridge collapsing. He asks his students why they think the bridge
collapsed. In giving their answers, the students reveal their preconceptions
about structure. Differences in their answers provide puzzles that engage
the students in self-questioning. As the students study structure, they can
mark their changing understanding against their initial beliefs. Assessment in
this sense provides a starting point for additional instruction rather than a
summative ending. Formative assessments are often referred to as "class-
room-based assessments" because, as compared with standardized assess-
ments, they are most likely to occur in the context of the classrooms. How-
ever, many classroom-based assessments are summative rather than formative
(they are used to provide grades at the end of a unit with no opportunities to
revise). In addition, one can use standardized assessments in a formative
manner (e.g., to help teachers identify areas where students need special
help).
Ultimately, students need to develop metacognitive abilities--the habits
of mind necessary to assess their own progress--rather than relying solely
on external indicators. A number of studies show that achievement improves
when students are encouraged to assess their own contributions and work.24
It is also important to help students assess the kinds of strategies they are
using to learn and solve problems. For example, in quantitative courses such
as physics, many students simply focus on formulas and fail to think first
about the problem to be solved and its relation to key ideas in the discipline
(e.g., Newton's second law). When students are helped to do the latter, their
performance on new problems greatly improves.25
The classroom interactions described in the following chapters provide
many examples of formative assessment in action, though these interactions
are often not referred to as assessments. Early activities or problems given to
students are designed to make student thinking public and, therefore, ob-
servable by teachers. Work in groups and class discussions provide students
with the opportunity to ask each other questions and revise their own think-
ing. In some cases, the formative assessments are formal, but even when
informal the teaching described in the chapters involves frequent opportuni-
ties for both teachers and students to assess understanding and its progress
over time.
Community-Centered Classroom Environments
A community-centered approach requires the development of norms
for the classroom and school, as well as connections to the outside world,
that support core learning values. Learning is influenced in fundamental
ways by the context in which it takes place. Every community, including
classrooms and schools, operates with a set of norms, a culture--explicit or
implicit--that influences interactions among individuals. This culture, in turn,

18 HOW STUDENTS LEARN
BOX 1-6 Organizing Knowledge Around Core Concepts: Subtraction with
Regrouping26
A study by Ma27 compares the knowledge of elementary mathematics of teachers in the
United States and in China. She gives the teachers the following scenario (p. 1):
Look at these questions (52 ­ 25; 91 ­ 79 etc.). How would you approach
these problems if you were teaching second grade? What would you say
pupils would need to understand or be able to do before they could start
learning subtraction with regrouping?
The responses of teachers were wide-ranging, reflecting very different levels of un-
derstanding of the core mathematical concepts. Some teachers focused on the need for
students to learn the procedure for subtraction with regrouping (p. 2):
Whereas there is a number like 21 ­ 9, they would need to know that you
cannot subtract 9 from 1, then in turn you have to borrow a 10 from the
tens space, and when you borrow that 1, it equals 10, you cross out the 2
that you had, you turn it into a 10, you now have 11 ­ 9, you do that
subtraction problem then you have the 1 left and you bring it down.
Some teachers in both the United States and China saw the knowledge to be mas-
tered as procedural, though the proportion who held this view was considerably higher in
the United States. Many teachers in both countries believed students needed a concep-
tual understanding, but within this group there were considerable differences. Some
teachers wanted children to think through what they were doing, while others wanted
them to understand core mathematical concepts. The difference can be seen in the two
explanations below.
They have to understand what the number 64 means. . . . I would show
that the number 64, and the number 5 tens and 14 ones, equal the 64. I
would try to draw the comparison between that because when you are
doing regrouping it is not so much knowing the facts, it is the regrouping
part that has to be understood. The regrouping right from the beginning.
This explanation is more conceptual than the first and helps students think more
deeply about the subtraction problem. But it does not make clear to students the more
fundamental concept of the place value system that allows the subtraction problems to
be connected to other areas of mathematics. In the place value system, numbers are
"composed" of tens. Students already have been taught to compose tens as 10 ones,
and hundreds as 10 tens. A Chinese teacher explains as follows (p. 11):
What is the rate for composing a higher value unit? The answer is simple:
10. Ask students how many ones there are in a 10, or ask them what the
rate for composing a higher value unit is, their answers will be the same:
10. However, the effect of the two questions on their learning is not the

INTRODUCTION 19
same. When you remind students that 1 ten equals 10 ones, you tell them
the fact that is used in the procedure. And, this somehow confines them to
the fact. When you require them to think about the rate for composing a
higher value unit, you lead them to a theory that explains the fact as well
as the procedure. Such an understanding is more powerful than a specific
fact. It can be applied to more situations. Once they realize that the rate of
composing a higher value unit, 10 is the reason why we decompose a ten
into 10 ones, they will apply it to other situations. You don't need to
remind them again that 1 hundred equals 10 tens when in the future they
learn subtraction with three-digit numbers. They will be able to figure it
out on their own.
Emphasizing core concepts does not imply less of an emphasis on mastery of pro-
cedures or algorithms. Rather, it suggests that procedural knowledge and skills be orga-
nized around core concepts. Ma describes those Chinese teachers who emphasize core
concepts as seeing the knowledge in "packages" in which the concepts and skills are
related. While the packages differed somewhat from teacher to teacher, the knowledge
"pieces" to be included were the same. She illustrates a knowledge package for sub-
traction with regrouping, which is reproduced below (p. 19).
The two shaded elements in the knowledge package are considered critical. "Addi-
tion and subtraction within 20" is seen as the ability that anchors more complex problem
solving with larger numbers. That ability is viewed as both conceptual and procedural.
"Composing and decomposing a higher value unit" is the core concept that ties this set
of problems to the mathematics students have done in the past and to all other areas of
mathematics they will learn in the future.
Subtraction
with regrouping of large
numbers
Subtractions with regrouping of
numbers between 20 and 100
The composition of Subtraction without
numbers within 100 regrouping
Addition and subtraction
within 20
The rate of composing Addition without carrying
a higher value unit
Addition and subtraction
within 10
The composition of 10
Composing and decomposing
a higher value unit
Addition and subtraction
as inverse operations
SOURCE: Ma (1999). Illustration reprinted with permission of Lawrence Erlbaum Associates.

20 HOW STUDENTS LEARN
mediates learning. The principles of How People Learn have important im-
plications for classroom culture. Consider the finding that new learning builds
on existing conceptions, for example. If classroom norms encourage and
reward students only for being "right," we would expect students to hesitate
when asked to reveal their unschooled thinking. And yet revealing precon-
ceptions and changing ideas in the course of instruction is a critical compo-
nent of effective learning and responsive teaching. A focus on student think-
ing requires classroom norms that encourage the expression of ideas (tentative
and certain, partially and fully formed), as well as risk taking. It requires that
mistakes be viewed not as revelations of inadequacy, but as helpful contri-
butions in the search for understanding.28
Similarly, effective approaches to teaching metacognitive strategies rely
on initial teacher modeling of the monitoring process, with a gradual shift to
students. Through asking questions of other students, skills at monitoring
understanding are honed, and through answering the questions of fellow
students, understanding of what one has communicated effectively is strength-
ened. To those ends, classroom norms that encourage questioning and al-
low students to try the role of the questioner (sometimes reserved for teach-
ers) are important.
While the chapters in this volume make few direct references to learn-
ing communities, they are filled with descriptions of interactions revealing
classroom cultures that support learning with understanding. In these class-
rooms, students are encouraged to question; there is much discussion among
students who work to solve problems in groups. Teachers ask many probing
questions, and incorrect or naïve answers to questions are explored with
interest, as are different strategies for analyzing a problem and reaching a
solution.
PUTTING THE PRINCIPLES TO WORK IN THE
CLASSROOM
Although the key findings from the research literature reviewed above
have clear implications for practice, they are not at a level of specificity that
would allow them to be immediately useful to teachers. While teachers may
fully grasp the importance of working with students' prior conceptions, they
need to know the typical conceptions of students with respect to the topic
about to be taught. For example, it may help history teachers to know that
students harbor misconceptions that can be problematic, but those teachers
will be in a much better position to teach a unit on exploration and discov-
ery if they know specifically what misconceptions students typically exhibit
and how these typically change with age.
Moreover, while teachers may be fully convinced that knowledge should
be organized around important concepts, the concepts that help organize

INTRODUCTION 21
their particular topic may not be at all clear. History teachers may know that
they are to teach certain eras, for example, but they often have little support
in identifying core concepts that will allow students to understand the era
more deeply than would be required to reproduce a set of facts. To make
this observation is in no way to fault teachers. Indeed, as the group involved
in this project engaged in the discussion, drafting, and review of various
chapters of this volume, it became clear that the relevant core concepts in
specific areas are not always obvious, transparent, or uncontested.
Finally, approaches to supporting metacognition can be quite difficult to
carry out in classroom contexts. Some approaches to instruction reduce
metacognition to its simplest form, such as making note of the subtitles in a
text and what they signal about what is to come, or rereading for meaning.
The more challenging tasks of metacognition are difficult to reduce to an
instructional recipe: to help students develop the habits of mind to reflect
spontaneously on their own thinking and problem solving, to encourage
them to activate relevant background knowledge and monitor their under-
standing, and to support them in trying the lens through which those in a
particular discipline view the world. The teacher­student interactions de-
scribed in the chapters of this volume and the discipline-specific examples
of supporting students in monitoring their thinking give texture to the in-
structional challenge that a list of metacognitive strategies could not.
INTENT AND ORGANIZATION OF THIS VOLUME
In the preface, we note that this volume is intended to take the work of
How People Learn a next step in specificity: to provide examples of how its
principles and findings might be incorporated in the teaching of a set of
topics that frequently appear in the K­12 curriculum. The goal is to provide
for teachers what we have argued above is critical to effective learning--the
application of concepts (about learning) in enough different, concrete con-
texts to give them deeper meaning.
To this end, we invited contributions from researchers with extensive
experience in teaching or partnering with teachers, whose work incorpo-
rates the ideas highlighted in How People Learn. The chapter authors were
given leeway in the extent to which the three learning principles and the
four classroom characteristics described above were treated explicitly or
implicitly. The authors chose to emphasize the three learning principles
explicitly as they described their lessons and findings. The four design char-
acteristics of the How People Learn framework (Figure 1-2) are implicitly
represented in the activities sketched in each of the chapters but often not
discussed explicitly. Interested readers can map these discussions to the
How People Learn framework if they desire.

22 HOW STUDENTS LEARN
While we began with a common description of our goal, we had no
common model from which to work. One can point to excellent research
papers on principles of learning, but the chapters in this volume are far
more focused on teaching a particular topic. There are also examples of
excellent curricula, but the goal of these chapters is to give far more atten-
tion to the principles of learning and their incorporation into teaching than
is typical of curriculum materials. Thus the authors were charting new terri-
tory as they undertook this task, and each found a somewhat different path.
History is treated in three chapters. The introductory Chapter 2 treats the
principles of learning as they apply to the discipline of history in impressive
depth. Elementary and middle school history are treated together at length
in Chapter 3, a decision that permits the authors to demonstrate progression
in the sophistication with which the same concept can be discussed at differ-
ent grade levels. Chapter 4 on high school history then follows, also focused
on the treatment of particular concepts that fall under the general topic of
exploration and discovery. Because there is no agreed-upon sequence of
topics in history during the K­12 years, using a single broad topic allows for
a clearer focus on the nature of the investigations in which students might
engage at different grade levels.
The major focus of the volume is student learning. It is clear that suc-
cessful and sustainable changes in educational practice also require learning
by others, including teachers, principals, superintendents, parents, and com-
munity members. For the present volume, however, student learning is the
focus, and issues of adult learning are left for others to take up.
The willingness of the chapter authors to accept this task represents an
outstanding contribution to the field. First, all the authors devoted consider-
able time to this effort--more than any of them had anticipated initially.
Second, they did so knowing that some readers will disagree with virtually
every teaching decision discussed in these chapters. But by making their
thinking visible and inviting discussion, they are helping the field progress
as a whole. The examples discussed in this volume are not offered as "the"
way to teach, but as approaches to instruction that in some important re-
spects are designed to incorporate the principles of learning highlighted in
How People Learn and that can serve as valuable examples for further dis-
cussion.
In 1960, Nobel laureate Richard Feynman, who was well known as an
extraordinary teacher, delivered a series of lectures in introductory physics
that were recorded and preserved. Feynman's focus was on the fundamental
principles of physics, not the fundamental principles of learning. But his
lessons apply nonetheless. He emphasized how little the fundamental prin-
ciples of physics "as we now understand them" tell us about the complexity
of the world despite the enormous importance of the insights they offer.

INTRODUCTION 23
Feynman offered an effective analogy for the relationship between under-
standing general principles identified through scientific efforts and under-
standing the far more complex set of behaviors for which those principles
provide only a broad set of constraints:29
We can imagine that this complicated array of moving things which consti-
tutes "the world" is something like a great chess game being played by the
gods, and we are observers of the game. We do not know what the rules of
the game are; all we are allowed to do is to watch the playing. Of course,
if we watch long enough, we may eventually catch on to a few of the rules.
The rules of the game are what we mean by fundamental physics. Even if
we knew every rule, however, we might not be able to understand why a
particular move is made in the game, merely because it is too complicated
and our minds are limited. If you play chess you must know that it is easy
to learn all the rules, and yet it is often very hard to select the best move or
to understand why a player moves as he does. . . . Aside from not knowing
all of the rules, what we really can explain in terms of those rules is very
limited, because almost all situations are so enormously complicated that
we cannot follow the plays of the game using the rules, much less tell what
is going to happen next. (p. 24)
The individual chapters in this volume might be viewed as presentations
of the strategies taken by individuals (or teams) who understand the rules of
the teaching and learning "game" as we now understand them. Feynman's
metaphor is helpful in two respects. First, what each chapter offers goes well
beyond the science of learning and relies on creativity in strategy develop-
ment. And yet what we know from research thus far is critical in defining the
constraints on strategy development. Second, what we expect to learn from
a well-played game (in this case, what we expect to learn from well-concep-
tualized instruction) is not how to reproduce it. Rather, we look for insights
about playing/teaching well that can be brought to one's own game. Even if
we could replicate every move, this would be of little help. In an actual
game, the best move must be identified in response to another party's move.
In just such a fashion, a teacher's "game" must respond to the rather unpre-
dictable "moves" of the students in the classroom whose learning is the
target.
This, then, is not a "how to" book, but a discussion of strategies that
incorporate the rules of the game as we currently understand them. The
science of learning is a young, emerging one. We expect our understanding
to evolve as we design new learning opportunities and observe the out-
comes, as we study learning among children in different contexts and from
different backgrounds, and as emerging research techniques and opportuni-
ties provide new insights. These chapters, then, might best be viewed as
part of a conversation begun some years ago with the first How People Learn

How Students Learn: History in the Classroom builds on the discoveries detailed in the best-selling How People Learn. Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness.

The book explores the importance of balancing students' knowledge of historical fact against their understanding of concepts, such as change and cause, and their skills in assessing historical accounts. It also features illustrated suggestion for classroom activities.

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